I don't know a name, but I know the song you're talking about. The lyrics I remember differ a bit from yours, but I suppose there were probably many slightly different versions of it all over the country. My grandmother used to sing it, and I believe that the lyrics she used were

"she stood out there in the midnight air,
and the wind it whistled up her nighty,
and the moonlight lit up the center of her tit
jesus christ almighty"

or something close to that. It seems to me I might be missing a word or two from the last line, but I'll be darned if I can remember any more than that.